Back to speaking like humans, the thing you are not responding to is expectations vs reality. Participation trophies are near ubiquitous in places like the US, and there's an ongoing attack on merit across a wide array of domains - let alone efforts to recognize and reward it. Were this having the effects you claim, would you not expect to see absolutely skyrocketing sports participation? In reality it's down, in many areas sharply so.
Before replying to expectations vs reality, we need to establish and agree on facts. Are you saying that in US, across all states and all sports, competition prizes has been replaced by participation trophies and you see a negative trends in sports participation?
And no I'm (obviously?) not speaking of every single instance, as for a topic like this there will always be some exception or another. I am saying that as an aggregate - sports participation is down, and participation trophies are up.
Same goes for other key needs in SDT – autonomy being most important. Here is a study of swimmers and their drop-out after 10 and 22 months after assessing their coaching styles (autonomous vs controlled). [1]
Competition prizes are also form of extrinsic motivation ("external regulation" to be specific). Extrinsic motivation can be (and often is) very powerful. It just don't last.
[1] https://www.researchgate.net/publication/225153306_Associati...